Tag Archives: lens grinding

As some know, primarily last summer I spent my time researching and theorizing on Spinoza’s lensgrinding and optical concepts, a largely underdeveloped field in Spinoza studies. The greater portions of my findings are listed here on this site under the sub-heading Spinoza’s Foci. A spearpoint of this research was uncovering the substantive arguments and conceptions that lay behind Spinoza’s rejection of Descartes’ optics, as found in his two letters 39 and 40, letters that have be nearly completely ignored by commentators on Spinoza, or if address, addressed in what seems a delinquent, or dismissive fashion. Spinoza is mostly thought to not know what he is talking about. On the other hand, Spinoza’s objections if carefully examined reveal both technically an alternate position on the problem of “spherical aberration,” but more deeply, a radically distinct conception of what vision is, in particular how it works as an insufficient analogy for consciousness. While Descartes wanted to emphasize the power of the central clarity powers of hyperbolic vision (both in the human eye, and in his proposed lenses), Spinoza understood vision and conciousness both as holistic events, ones best approached with the pragamatic appreciation of our limitations. I provide very little philosophical extrapolation here, though the implications are vast, perhaps running through down to the root of Idealism and Phenomenology. This epistolary commentary also does not touch on such other important factors such as the kind of lathe Spinoza likely used, nor much on his likely technique, and kinds of instruments he made and calculated for, which form a significant secondary branch of my research. Yet as these letters remain nearly the only first hand statement Spinoza made on optical matters, they are the anchorage point for anything else that is likely to be asserted.

For the convience of interested readers I here post a Word document version of my line-by-line explication of these rarely read and rather under-interpreted letters. I realized that the previous weblog versions were very difficult to read and browse through, hopefully something this version will correct. The two entries that can be found in this document are: Deciphering Spinoza’s Optical Letters and Spinoza: Letter 40 and Letter 39. These are both the English translation of the two letters by Spinoza, and then my explication. This version is not footnoted (though there are citations), and it retains some of the idiocyncratic paragraphing and color coding. It is a 14,000 word document (48 pages), though Spinoza’s letters are only 900 words or so.

It has been revealed by some digging into the record by Stan Verdult that indeed the lathe that occupies the Rijnsburg Spinoza museum is not of the sort Spinoza would have used (though it may give us a sense of the size of his lathe). [Written about here: The Rijnsburg Lathe: Like the Sun, not 200 Feet Away .] But if we are to come close to understanding the near-daily physical practices Spinoza had engaged in as a lens-grinder and maker of both telescopes and microscopes, we need to narrow the view to the design parameters his grinding lathe likely exhibited. I have mentioned in the past that the foot-driven lathe of Hevelius, as published in his astronomical study of the moon, Selenographia (1647), provides us perhaps of the most revealing illustration of the elements that would have been involved.

We know from Spinoza’s comments on the semi-automated designs of Christiaan Huygens whose home in Voorburghe certainly seems to have visited multiple times, that Spinoza favored a simple grinding mechanism, one in which the glass to be ground was held freely in the hand (affixed to a handle). The general disposition among mid-century savants to further automate the grinding process and remove the human element from the process as much as possible seems to have been looked on withextreme doubt by Spinoza. This does not mean that there was no automated aspects to Spinoza’s lens-lathe, for the lathe itself is a machined dynamic which transfers motions by the hand or the foot to a concentric movement put upon the glass blank. It is only that Spinoza preferred the moment-to-moment, lived craft judgments that came from an artisan’s practice through the encounter withthe machine. In this way our focus should be upon the nature of the machine/human interfaces used by Spinoza, and therefore a central question is whether Spinoza used a hand-driven or foot-driven lathe, with a view to visualizing each as vividly as possible.

Foot-driven lathes were not uncommon in the era, in fact Hevelius’ Illustration of his lathe was published when Spinoza was 15 years old, perhaps a decade before his reported lens-grinding days, and likely was not seen as an innovation then. I suggest that it is to this illustration we must turn if we are to get a clear picture of the kind of physical actions Spinoza trained his eye upon.

the lathe as it appears in Hevelius's Selenographia

In the labeled illustration below, one can see the general action of the foot pedal transfer of power to a concentric motion, and the orientation Spinoza may have had, and the pole that may have been fixed to the ceiling of his room:

Here are various details so as to better see the composition of components:

Here one can see the transfer of the cord to a grinding form’s modular base. It would not be necessary, or even likely that this modularity would be a feature of Spinoza’s lathe, but the horizontal orientation of the grinding dish (as opposed to the vertical angle shown in designs from earlier in the century) would be the preferred design, for this would allow gravity to act as ally in abrasive control and arm fatigue. (We do not know how intermittent Spinoza’s tuberculosis was, a disease that he, by Colerus’s account, suffered from since about the age of 24, but the question of endurance could have been a singificant factor in the kind of lathe Spinoza used.)

In this close-up to the foot pedal one can see the simple nature of the drive mechanism. A foot pedal allows of course one to use the larger leg muscles, a benefit for more arduous projects; but it also informs a vertical tension from the floor to the ceiling. There is a cross dynamic between the communications of the foot to the spring pole high above, which is then read in the relative speeds and intensities by the hand pressing its material downward. The oscillations of upward and downward, a horizontal, yet fixed, stable circular whirrings do suggest a grid of complex physical actions and interface. One may be tempted to see in this cross-dynamic the metaphysics of the verticality of Substanced expression, and the horizontality of modal causations. In any case, the foot pedal lathe leaves a distinct epistemo-kinetic imprint upon the craftsman that engages it, something that surely would have informed Spinoza’s thinking about material and its formation.

Yet on the level of information on technique, perhaps even of more interest in this close up of the Hevelius drawing is the shape of the grinding forms discs placed haphazardly on the floor. They are not the hollowed-out concave metal forms like those, let us say, Hieronymus Sirturus wrote about in his influential book on technique Telescopium, siue Ars perficiendi nouum illud Galilaei visorium instrumentum ad sydera(1618), (whose spherical perfection was created by being ground against a matching convex iron casting). They appear instead concavely beveled, on the inner slope of which a lens can be angled to be ground (if I read the illustration correctly).

One can see each of these types of grinding forms (a beveled inner edge, and the scalloped dish) in van Gutschoven’s 1663 letter to Christian Huygens which had answered Christiaan’s question as to how to grind smaller objective lenses [comments on: A Method of Grinding Small, Spherical Lenses: Spinoza ]:

Here in the van Gutschoven illustraton a narrow canal (vertically aligned) serves as the grinding surface just inside the lip.

And here is a concave finishing form, in whose center a small lens would be placed for polishing. The two illustrations above simply show that both form designs were employed, and we cannot be sure if Spinoza would have used one or the other, or both (though the degree of curvature shown above would be wholly inappropriate for telescope lenses for which only a slight curvature was needed). One might add, by Spinoza’s use of the terms “dishes” or “plates” for his metal laps, the scalloped spherical form, hollow at the center, one could presume was a main metal form that he used.

To return to the Hevelius example, if we can seriously entertained the prospect that Spinoza used a foot-pedal grinding lathe, I would want to point out the thorough and bodily engagement that grinding would have involved. Not only were the powers of close-eyed concentration, and precise fingered and armed exertions involved, but also a co-ordinated rhythm between the actions of the foot that from a distance below swiveled the grinding form back and forth, reversing itself, restrained from high above, bringing fortha total read of machine tensions which completed a lived circuit between the human body and its attentive results. Spinoza’s entire body would be in play in the workings of the glass, from head to toe. And if one superimposes the requirements of his metaphysics (his equivocal treatment of Thought and Extension, and his definitions of a body and power) upon this organization of machine, idea and flesh, one may see with growing clarity how his crafted practices informed his most abstract thinking.

This is the case found in the Hevelius example, which forms one end in the spectrum of the possible machine designs Spinoza likely used. There is of course a much simpler design, the hand-driven lathe, which Spinoza may have also worked from. The nature of this lathe can be seen in the 1660 Manzini manuscript, and the expert mock up made by the 400th Anniversary of the Telescope team:

One can see the typical concave metal dish (to the left) and the hand-drive of the form. In terms of dynamics instead of a swivel motion to the form, a repeated back and forth oscillation driven by the foot co-ordinated from high above, here the form can be spun in continuing circles in close proximity to the chest. Evidence that Spinoza used just such a design perhaps can be seen in the list of things sold from his estate in November of 1672.

and various instruments for grinding (‘en verscheidene slypgereedschap’) like mills (‘molens’, also plural!) and great and small metal dishes serving for them (‘groote en kleine metale schotels daartoe dienende’) and so on” (en so voort).

That there were multiple mills sold (not a complete list of what he owned one might assume) suggests a variety of more specialized devices, instead of one large workbench as that shown in the Hevelius example. But this is not at all a clear, or exclusive conclusion. Small hand-driven grinding lathes may have been employed for small microscope objectives (which Spinoza favored) or telescope eye-pieces, whereas a foot pedaled, spring pole machine could have been used for larger telescope glasses which could reach nearly 1/2 a foot in diameter.

In digression, there is evidence that Spinoza collaborated with the respected optical mathematician and amateur scientist Johannes Hudde on calculations for a 40 ft lens. To give a sense of it, such a lens would have been approximately 5 inches in diameter, of very slight curvature and only 5 – 8 mm thick: Huygens’s letter to his brother 23 Sept 1667:“Ie voudrois scavoir quelle grandeur d’ouuerture Spinosa et Monsieur Hudde determinent pour les 40 pieds” (See “The Lens Production of Christiaan and Constantijn Huygens” , 1998, by van Helden and van Gent, for the dimensions of similar lenses). Whether Spinoza was in the practice of grinding such lenses, which at the time would have been among the most powerful telescope lenses in Europe, we cannot know. But it seems he was involved in their calculation.

To return, if we are to imagine a hand-driven lathe’s effect upon Spinoza’s rational conception of Mind and Body relations, the form’s spinning, instead of oscillating, motion, may involve less of the entire body than a foot pedal lathe would; the head, the shoulders, the hands would form a frame of power and sensitivity, withthe shoulders acting as fulcrum points of stability and the hands as reading extensions. The cybernetic feedback between the hands, one holding the glass blank, the other whirling in circles would seem to be even more involved, more kinetically woven than that of the foot pedal lathe. The power transfer is more direct the thus the communication between hands more intimate. And one sees how the manifestations of concentric stability and change, eternity and flux, expressed in two respondent revolving discs, certainly could present itself as significant to the circle-loving craftsman as he sought to perfect his lens under physical pressure and frictions of grit.

By my view it seems most likely that Spinoza employed both kinds of lathes, the foot and the hand driven, perhaps at different points in his life, in a process of a refining of techniques. What really is at stake in this analysis I would contend is that one must be able to SEE what Spinoza did during a preponderance of his days, picture it physically, in an affective projection, to fully conceive what he thought. The machine and the human, that mind in the device and the matter of the idea understood to be in mutual conjunction.

An initial synthesis of some of the aspects of my research and a more refined notion of craftsmanship: writing to think through.

This is not the place to write a review of Richard Sennett’s provocative, subtly powerful book The Craftsman. I can only say in that vein, it is a book I highly recommend for those who enjoy looking at recurrent themes in culture and technology, wih an eye to informed thinking about the challenges and opportunities that face us today. The book is chock-full of illuminating analogies and narratives of human progress in problem solving [what he does with chicken recipes is astounding]. Aside from this general appreciation I believe Mr. Sennett’s observations on the significance of the wisdom of the craftsman has great consonance with the same point I am have been attempting to establish: Spinoza’s view of seeing technology as a continuous interface between bodies in assemblage. To put it one way the Craftsman represents the bodily knowledge shore between ideas held and our capacity to act, something I believe is embraced by Spinoza’s parallel grasp of both Mind and Body, thought and extension.

But from this book I would like to concentrate on a few distinctions of analysis Sennett makes to study they way that tools are used, and to assess their epistemic value as a means of intuition and inference. I cite from his chapter “Arousing Tools”.

Mr. Sennett starts with a general appraisal of the place of tools in our process of learning and acting:

Getting better at using tools comes to us, in part, when the tools challenge us, and this challenge often occurs just because the tools are not fit-for-purpose. They may not be good enough or it’s hard to figure out how to use them. The challenge becomes greater when we are obliguedto use these tools to repair or undo mistakes. In bothcreationand repair, the challenge can be met by adapting the form of a tool, or improvising with it as it is, using it in ways it was not meant for. However we come to use it, the very incompleteness of the tool has taught us something (194).

He goes onto make a distinction between a fit-for-purpose tool and an all-purpose tool. The example he uses for each is a screwdriver. A philips-head screwdriver is fit for one purpose, yet a flat-blade driver has a flexibility to it, “it can gouge, lift, and line as well as screw”. It is tempting to apply Spinoza’s definition of power to this distinction, the flat-blade tool actually has a greater number of ways it can “affect or be affected”. This does not make it a better tool at any given instance, for it its capacities must be assessed in assemblage to situations and to among other things, screws, but there does seem to be a fundamental difference to be noted.

The all-purpose tool has something of an openness to it:

…in its sheer variety this all-purpose tool admits all manner of unfathomed possibilities: it, too, can expand our skills if only our imagination rises to the occasion. Without hesitation, the flat-edged screwdriver can be described as sublime – the word sublime standing, as it does in philsophy and the arts, for the potentially strange. In craftwork, that sentiment focuses especially on objects very simple in form that seemingly can do anything.

I’d like to stop here for a moment, for I am attempting to look through Richard Sennett’s lens at the discoveries I have come upon in regard to Spinoza’s technical-optical practices. There is no doubt that Spinoza, at least in life, if not in philosophical theory, embodies the core values of the craftsman. He lived a thrift life upon the intentionally thin thread of the earnings of his lens-grinding and instrument making. He came from the artisan class of Amsterdam Sephardic Jewry, and devoted himself to the perfection of things for their own sake, a mark of craftsmanship. And his hands-on experiences with materials and the lathe gave him a distinctly craftsman approach to problems of light and glass. If we ask, For Spinoza, what tools would strike him as “sublime” in the sense that Sennett defines it? It would seem safe to say that the lathe in its simplicity and multiplicity of uses would be sublime. Nearly every required lens could be ground on his bench provided the right glass, abrasives and forms were available. This spinning concentric action must have been “potentially strange” and a source of many, perhaps unconscious, inferences.

I think though that in my close reading of Spinoza’s two Optical Letters, it would seem that Spinoza also regarded the spherical lens as sublime. In his argument for its superiority its essential multiplicity, as long as one accepted its one inherent drawback of slight spherical aberration, gave it a certain panopticalquality, the way that it addressed rays coming from all points of a field of view. One can say that this understanding came from a failure to properly understand the optics involved, but I suspect that it is rather overestimated how correct the understanding of contemporary optics was. A theorist could hold what we take to be a “true” optical belief, but only due to fact that he also held a great number of beliefs we would regard as false. In a sense, to assess the truth or falsity of a scientific belief, one should perhaps take a more tool-oriented view toward these beliefs, asking how they worked to solve which problems.

Keeping this in mind, I think it safe to say that Descartes’ also found his discovered (imagined) hyperbolic lens “sublime”. For Descartes the simplicity of its form (a hyperbola could be made with two sticks and string in the garden he tells us), the elegance of its line bespoke a remarkable potential for applicability. But there is something to the foundational thinking of Descartes’ hyperbola (shown in Kepler), which also seemed to make it something like a fit-for-purpose tool, a philips-head. The way that Descartes saw it, it matched the human eye, acting like a hand and glove prosthetic extension of the organ out into space. It fit its purpose. Additionally to this, it not only fit the shape and powers of the eye, but it also snugly secured itself within Descartes larger conception of perception and the exercise of the Will. The hyperbola’s narrow aim of focus matched Descartes’ idea of the “clear and distinct” object of perception, crispened in a field of obscured images. This field was a background for the exercise of valuations and free choice. It was this fit-for-purpose aspect of the lens that I believe Spinoza instinctively had some objection to. It could be argued that Spinoza’s embrace of spherical lenses also had a fit-for-purpose quality to it, as indeed it did. The sphere was evocative of the completeness of mental-vision that in the pre-requisite acceptance of inadequate and imaginary ideas, strived for a total awareness of the causal matrices that brought things together. What needs to be pointed out is that Spinoza is not the only holder of such conceptual relations. Rather, they are likely endemic to all descriptive, problem-solving thought. At the time the understanding of refraction and spherical aberration was still quite confused, even in the minds of those that would make the most progress in these areas.

In a certain way, Mr. Sennett wants us to know that the very ambiguity of a tool, the fuzziness of its ability to work, is that which stimulates us to imagine what must be the case that would make the tool work (or require a new tool). He tells a wonderful story about the problems that arose with the invention the surgical scalpel (15th century), born of the introduction of silica into the iron, giving a new and remarkable sharpness. It enabled precise anatomical dissections and discovery, as well as advances in living operations. Remarkably this new knife produced the difficulty of now to cut, what techniques of muscle movements could handle this suddenly fine instrument (less shoulder and a co-operations of figures Sennett tells us). It seems it took a century or more to be able to master these new powers. The tool imposes itself upon the imagination in the context of the resistances of the world.

It is easy to think that Descartes had in mind that his hyperbolic lens would act something like the new scalpel, like his hyperbolic doubt, it would cut through the murky imperfections of the field and clearly select out what is essential. It would carry the eye to distant things, by extending the eye itself. Generally it is assumed that Descartes valuably got it right with the hyperbola, as he identified a solution to spherical aberration (already pointed out by Kepler). And if we are to imagine that he got it wrong, there are likely two ways he was wrong. The first was the widely assumed connection between what turned out to be chromatic aberration (the obscuringcolored ring in telescope observations), and spherical aberration. But, as Graham Burnett has pointed out, he also got wrong his assumption that he could just take a mathematical formula, engineer on paper a machine that could would carry it out, and with a little advice and sweat from a hired craftsman, his paradisaical lens could easily be produced. Again and again he expressed frustration with hired artisans that either they or the materials were failing him.

Four Stages

Sennett gives us a guide to stages of technological development that might help us see Descartes difficulty more clearly, and perhaps gain the value of Spinoza’s craft-sensitive, if metaphysical objections. First he says that there is reformatting. Reformatting is simply the “willingness to see if a tool or practice can be changed in use”. The example offered is the way that Christopher Wren used chiaroscuro techniques of shading in his illustrations of specimens shown in Robert Hooke’s microscope, so to produce plates more vivid than what could actually have been seen in the poor quality glass and light, while still being perceivedas quite accurate. Descartes indeed employed reformatting in both his development of mathematical tools (a forwarding of the Law of Refraction), and his inventive design of an automatic lens-lathe, but lacked any capacity to reformat techniques of placing materials in relation to each other in real machines, assuming that this was the least difficult portion of the process, just getting the matter to do what the mind wished it to.

Secondly, there is adjacency. “Two unlike domains are brought close together; the closer they are, the more stimulating their twined presence”. This seems precisely what Descartes did in terms of his imagination of the eye and his hyperbolic lens. By placing the two hyperbolic forms, organic and glass, together in an assemblage, his inferences to the clarity of thought and vision took wide gallop.

Thirdly, is intuitive leap or surprise. “Although you were preparing for it you didn’t know in advance precisely what you would make of the close comparison. In this third stage you begin to dredging up a tacit knowledge into consciousness to to the comparing – and you are surprised. Surprise is a way of telling yourself that something you know can be other than you assumed” (211). This no doubt lead to the writing of the Dioptrics, and his more than decade-long pursuit of a grinding machine capable of making his very precise lens.

Fourth is Gravity. “The final stage is recognition that a leap does not defy gravity; unresolved problems remain unresolved in the transfer of skills and practices…The recognition that an intuitive leap cannot defy gravity matters more largely because it corrects a frequently held fantasy about technology transfer. This is that importing a procedure will clarify a murky problem; more often, the technical import, like any immigrant, will bring with it its own problems” It is in gravity that Descartes seems to have failed, and is there no better evidence of this than Descartes (feigned?) glee that his craftsman de Beaune had severely cut his hand trying to make the desired lens, proving to Descartes the superiority of his rational vision! Descartes lacked the connection to material practices to adequately transfer his familiar terrain of mathematics and geometry to lathes and glass. His lens was impossible to make.

These four stages help us enframe something of Descartes’ failings and also help suggest to us something of Spinoza’s resistance to the lens and its attendant conceptions. There is one more tidbit that Richard Sennett offers us in this chapter that I want to bring to the issue. He says that in his distinction between a fit-for-purpose tool and an all-purpose tool, as they are designed specifically to either repair something broken or seek to improve it upon repair,

The tool that simply restores is likely to be put mentally in the toolbox of fit-for-purpose-only, whereas the all purpose tool allow us to explore deeper the act of making a repair. The difference matters because it signal two sorts of emotional responses we make to an object that doesn’t work. We can want simply to relieve its frustration and will employ a fit-for-purpose tool to do so. Or we can tolerate the frustration because we are now also curious; the possibilities of making a dynamic repair will stimulate, and the multi-purpose tool will serve as a curiosity’s instrument (200).

It is fair to say that both Spinoza and Descartes, in their philosophies, imagined the possibility of radical improvements in the minds and lives of their readers. Descartes’ radical doubt, and Spinoza’s “clear and distinct” excellerated leap to the Totality of Causes: God, are figured as sublime simplicities. And each thinker has characterized the process as that of the making of tools that could make other tools, like a blacksmith (Spinoza borrowing the image from Descartes). What I would want to ask would be, what is the role of the simplicity of craftsman understanding of the lathe and the lens in Spinoza’s vision of what is clear? For Spinoza I think it likely that he thought of the spherical lens as something like the flat-edged screwdriver, capable of a workman-like enhancement of human bodily powers. This all-purpose property allowed him to remain with this curiosity focused upon a more systematic and comprehensive vision of what made vision clear: the Ideas that we hold. I suspect that it was his hands-on practice of grinding glass to required mathematically describe shapes, and his physical understanding of the fancifulness of Descartes’ hyperbola, that lead him to disparage the enthusiasm for the shape. This did not prevent him from investigating it, but it did keep him in deep suspicion of metaphysical and scientific foundations of its importance.

I think also that this resistance to the hyperbola, and the fundamental acceptance of spherical aberration as a slight and perhaps necessary impairment, draws our attention to Spinoza’s understanding that real change occurs in the world of human imagination and affects, within the realities of our weaknesses. Despite his great concentration upon rationality and abstract reasoning, the model of Euclid’s Geometry, it is within human sociability that the hands touch the matter at hand. The realities of the properties of present conditions are the actual vectors of the power we may have. Any active use of reason does not transcend its earth. As he understood that any change in power and freedom requires a change in the body, and that any ideational move was a physical move, so must he to some degree have gleaned this understanding from the resistances of the cloudy glass and the spinning of the lathe, in the cybernetic feedback of his body’s own actions and experiences. The polishing of a lens was prosthetic, but not prosthetic to the eye, prosthetic and expressive of the body and mind.

I think that that in the gap between the two Substances of Descartes lies Spinoza at his lathe.

Reading Margaret Gullan-Whur’s often speculative, though quite vivid and deeply researched biography of Spinoza: Within Reason: A Life of Spinoza (1998), I see that she joins me in my loose intuition that Spinoza’s later translator Jan Glazenmaker may have been an influence in Spinoza learning how to grind lenses [offered up here:Jan Hendriksz Glazemaker…the Glazier ]. As she writes:

Such tools and materials were easily available in Amsterdam, and what other master would Benedictus need than Jan Glazemaker, friend of Van den Enden? Glazemaker, a Flemish Mennonite from a glass-making family living on the Prinsengracht, was now a Latin scholar. In recent years he had translated all Descartes’s available philosophy into Dutch. But when he married in 1651 he gave his profession as “glassmaker”, and only in 1687 was he registered in the poortersboek as a translator. While the textbooks on glass-cutting and optics that Spinoza owned were not published until 1663 and 1668, he must have made lenses before then, for in 1661 he was observed “to occupy himself with the constructions of telescopes and microscopes”, and the skills needed for that cannot have come easily. A three-year apprenticeship is still required for perfecting lens-grinding and polishing. In the mid-seventeenth century the arts of polishing and “peeping” were gentlemanly hobbies, to the chagrin of committed researchers (89).

It is of course nice to have one’s investigative musings supported by others, but I do have some questions about her observations. The first is her translation of Glazemaker’s name, as “glassmaker”. I have no knowledge of Dutch, but the occupation is most often translated as “glazier” which strictly is not a “glass-maker” (although I imagine that the two trades could be conflated). But whether he is a glazier in the more modern senseor not – cutting glass and fitting it into architecture and decorative design – I could see him being of help locating sources of glass, and how to cut it, but I cannot imagine that he would be a “Master” who could teach the art of glass lens polishing. Secondly, as I am unfamilar with the 1955 Twyman title she uses as a source on the history of glass cutting, I don’t know if its description is accurate to Spinoza’s time, but it does not coincide with the contemporaneous 17th century descriptions I have so far read, for instance those from Manzini or Rheita. (It is interesting though that diamond dust does make its appearance here for the first time in any of my research, apart from my very loose hypothesis that diamond polishers may have been a source for Spinoza’s knowledge.) As to the issue of the length of apprentice time, I do not follow which source Gullan-Wuhr uses for the three-year estimate for lens grinding proficiency (Twyman?). I do have a related uncited estimate that diamond polishing skill could have been learned in a time as short as 15 months. And Christiaan Huygens, after having learned the basics of lens-grinding from Gerard van Gutschoven in person, seems to have assimilated the whole of advanced lens-grinding from four pages of technical advice in a letter from van Gutschoven in January of 1653 (OC 1, 219-23). The brothers constructed their first telescope only two years later, in February of 1655: a telescope which was the most powerful in Europe, mighty enough to unveila moon and the rings of Saturn. There seems to be evidence that lens-grinding could be accomplished with some efficacy with rather limited apprenticeship. Yet, it would not at all seem likely that Glazemaker would have been the one who provided it for Spinoza.

As a side note, I must say that I am very enthused by Gullan-Whur’s citation of two lens-grinding and glass-cutting texts that Spinoza had in his library: Optica Promota, by James Gregory (1663) and Art of Glass-Cutting, [L’Arte Vetraria ] by Antonio Neri (1668).

Today, in contemplating Spinoza’s objection to Huygens’s semi-automated lens-grinding lathe (from Letter 32), and considering what it might mean for an overall Spinoza view of technology, I am struck by an immediate incongruity. Christiaan Huygens’s love of the mechanical, that is the ambition for the nearly direct implementation of the math to the material, through the correct devising of a means of transfer, seems to embody much that Spinoza would agree with. That is, both are determinative mechanists, and the proper construction of a mechanism would seem to be paramount in both thinkers view of how a lens should be ground. For one could say without too much occlusion, Spinoza thinks of the world being made up of two things: information (what he calls “Idea”), and matter (what he calls “extension”). The direct transfer of information to matter that technology seems to promise would seem to be exactly that Spinoza would favor.

But instead Spinoza baulks at the notion that the “free hand” of the craftsman should be removed from the process:

..what tho’ thusly he will have accomplished I don’t know, nor, to admit a truth, strongly do I desire to know. For me, as is said, experience has taught that with spherical pans, being polished by a free hand is safer and better than any machine (Letter 32).

One has to ask, is this just a technician’s sobriety, a conservative, “let’s see what it can do before we get too excited”? It seems not, for he really is not at all enthused to even find out. There seems a much more rooted objection, a tugging away from the simple connection between Idea (information) and Thing, that technology embodies. It is strange, because the minimization of the anthropological that Spinoza’s philosophy is most notable for comes right up against another principle, perhaps something we can call the principle of implementation. For Spinoza, because all technology is in combination with human beings, and its use a part of the human perception of the world and itself, in order for any technological process to be assessed, ALL elements of its assembled mechanism, including those of the state of the human beings involved, have to be considered. Because human beings do not form a “kingdom within a kingdom,” any device must be considered within the causal matrix of ideas and matter than make up its users and its practitioners. At least that is what I have come to believe Spinoza is thinking about, as he expresses reluctanceto remove the “free hand” from the process of crafting lenses. He is not against such a handless construction, but one senses that he is hesitant, holding in his view a greater scope of the issue at hand. For the 17th century desire to remove the craftman is not simply the desire to remove the “human error” from a process, but also is a labor calculation, suggestive of the Capitalist forms that were on the rise. The “free hand” question, is the question of interface, of communicative dialogue between the mechanism of gears and wheels and the mechanism of the human person (and community).

In a sense, what is at stake is the full consideration of interface. The impress of an idea (information) upon matter is a condition-dependent relation. One cannot simply press any kind of material into a spinning grinding mould to produce a lens. The specifics of the states of each must be appreciated. In this same sense there is a temporality, a historicity, to the transfer of ideas, one that Spinoza weighs as he wrote his first “rule for living” in the Emendation:

1. To speak to the understanding of the multitude and to engage in all those activities that do not hinder the attainment of our aim. For we can gain no little advantage from the multitude, provided that we accomodate ourselves as far as possible to their level of understanding. Furthermore, in this way they will give a more favorable hearing of truth.

His rule is to speak to the multitude, yet he will learn to not publish his Theological-Political Treatise in Dutch, keeping it from the multitude. Right away a differential comes apparent. The accomodation is really a measurement, a measurement that not only must be done with reason, but within the melieu of imaginary constructions and affective affinities. Perhaps this is why Spinoza is removed from the direct seduction of mechanical transfer. This is a finesse of his monist metaphysics. The transfer of ideas (information) to form, is never actually a transfer at all, but must be seen as an unfolding of two parallel Attributes. There is no descent into matter. Here Descartes and Spinoza radically diverge. Spinoza’s immanence becomes a line of permutation. The human element indeed has no hierarchical privilege in his Universe. It is shot through with error, but removing the human hand does not necessarily increase the power of an instrumental relation. This conceptualization of the human hand as a hand of error, of the craftsman as the ignorant purveyor unreflectant and unmodern traditions, a drag on the transcendent rise of Reason, is – I think Spinoza would say – an imaginary relation. For a machine to work properly, the free hand must always be located, and gauged.

The following is an exercise in historical imagination, only meant to elicit what is possible from what we know. Perhaps a fiction bent towards fact.

Wim Klever has brought to my attention a detail which sheds some light upon the possible lens polishing techniques Spinoza employed. Admittedly the connective tissue for a conclusion is not there, but the inference remains.

Professor Klever tells me that in his “Insignis opticus: Spinoza in de geschiedenis van de optica” he cites Freundenthal’s publication of the advertisement of the auction of the Spinoza’s estate in the Haarlemse Courant. The advertisement was printed on November 2nd, and occurred on November 4th (almost 9 months after Spinoza’s death). It seems likely that Constantijn Huygens jr., and/or his brother the famed scientist Christiaan, bid at and purchased what remained of Spinoza’s estate. This is how Wim Klever roughly translates some of the items:

books, manuscripts, telescopes (‘verrekyckers, mind the plural!), microscopes (‘vergrootglazen’, also plural), glasses so grinded (‘glazen soo geslepen’), and various instruments for grinding (‘en verscheidene slypgereedschap’) like mills (‘molens’, also plural!) and great and small metal dishes serving for them (‘groote en kleine metale schotels daartoe dienende’) and so on” (en so voort).

It is the number of devices and equipment that is Klever’spoint. Spinoza is not a dabbler in optics. He does not grind a few spectacle glasses for the near-sighted, but rather is interested in full-blown optical instrument production. There are multiple telescopes and microscopes to be had, as well as perhaps something more important, his grinding dishes, and at least two lathes or mills not to mention other small details of his process. Certainly the bill of sale attests to a rather thorough industrial investment on Spinoza’s part, making of his optical enterprises something quite substantial, but what I am most interested in here is the timing of this auction, in the view of the events that immediately are set to follow, events which may give clue to the nature of just what it is that Constantijn Huygens purchased for his brother.

Spinoza’s death, and auction occurs right at the doorstep of a very important moment in history: the official discovery of protozoa, bacteria, and then spermatozoa by Van Leeuwenhoek in nearby Delft. And it is this discovery which will eventually catapult the single lens simple microscope into European renown. But there is, I suggest, a good chance that Spinoza had been making, using, giving to others and possibly selling this kind of microscope for a very long while (Klever translates “vergrootglazen” as “microscope” as one should, but there is another word for microscope, and this word means “glass that magnifies” perhaps more suitable for a single lens microscope.)

First, I should point out that Christiaan Huygens had been a neighbor to Spinoza since 1663 when Spinoza moved to Voorburg, a sleepy village just outside ofThe Hague. He is a profound experimenter and scientist, having, among other remarkably brilliant things, invented the pendulum clock and discovered the rings of Saturn in the very same year of 1656. Spinoza had, most agree, become a conversational friendinthe summer of 1665, when the two of them discussed optical theory it seems with some regularity and detail. The Huygenses lived about a 5 minutes walk from Spinoza’s room at the house of master painter Daniel Tydeman, just down the road. Christiaan moved to Paris in 1666 to take the prestigious position of founding Secretary to Académie Royale des Sciences established by the Sun King Louis XIV to rival the Royal Society of London. There was no doubt extreme pressure to counter and surpass the great flow of knowledge that was collecting at the Royal Society under the supervision of Oldenburg.

During the intervening years, as Huygens attempted to bolster his Academy, in letters written to his brother back in Voorburg he expressed interest in Spinoza’s lens polishing technique. As early as 1667, he writes Constantijn “the [lenses] that the Jew of Voorburg has in his microscopes [I don’t have the original word here] have an admirable polish” and a month later again, “the Jew of Voorburg finishes his little lenses by means of the instrument and this renders them very excellent”. Here we have an attestation to both the mystery of the quality of Spinoza’s polish, (it was a technique which Spinoza apparently kept to himself); and also there is the hint that the instrument used was meant for very fine work, on the smaller of lenses. (In general, the difficulty in acquiring a fine polish on lenses was a significant aspect of lens-crafting technique, as polishing away the pitting of the glass brought in the grinding often would change the spherical shape of the lens.) In 1668 Christiaan then writes to his brother a concession over a debate that he must have been having with Spinoza, that Spinoza is right that the smallest objective lenses make the very best microscopes.

These references by Christiaan establish that the Huygens brothers’ had interest in techniques which Spinoza was not free with, and that Spinoza was on the side of the debate that theoretically would favor the use of single lens microscopes; this, at the very least, confirms their acquisition of his equipment and lenses to be something of a notable event. If there was anything to Spinoza’s technical capabilities which resided in the equipment he used (small grinding dishes, the nature of his lathe, an abrasive recipe, a polishing material), this fact might be evidenced by a sudden change in the capacities of either brother in making microscope lenses.

And remarkably, such a change was to come.

Now the issue of timing. Here is a timetable of events that led up to Christiaan Huygens presenting a “new microscope” to the Académie Royale des Sciences, one that perhaps reflects something of Spinoza’s technique in crafting lenses.

22 Feb. 1677 Van Leeuwenhoek’s letter 18 to the Royal Society is read aloud, the “first ever written account of bacteria” (Dobell).

August 1677 Van Leeuwenhoek discovers the animalcules in semen, spermatozoa

4 Nov. 1677Spinoza’s auction, the Huygenses seem to have acquired some of Spinoza’s equipment.@ 4 Nov. 1677Van Leewenhoek writes to the president of the Royal Society, William Brouncker, about his observation of the spermatozoa in semen. This sample was brought to him by Leiden medical student Johan Ham (who also might have had a single lens microscope).Late 1677 Christiaan expresses interest in the Van Leeuwenhoek/Ham discovery (OCCH 8:77; and 62-3, 65).

March 1678Hartsoeker explains to Christiaan how he makes lenses from beads of glass.

16 July 1678 Christiaan presents to the Académie Royale des Sciences the “new microscope” that differs from others in Holland and England only in the very small size of the lens.

Aug. 1678 Christiaan writes “my microscopes” have made a “great noise” in Paris.

One must know that single lens microscopes had already been in use in the Netherlands for some time before these dates. It had been used, but its capacity for magnification had not been regularly harnessed to make scientific discovery. Part of this was due to a difficulty in using it, for it must be pressed very closely to the eye, requiring great patience, and lighting techiques for the specimen in contrast had to be developed. And part of this dearth of scientific discovery was due to simply the lack of a conceptual framework for the microscopic world. This was a new world. Few as yet would even know where and why to point such a small and powerful viewing glass. Be that as it may, the microscope technique of forming tiny bead lenses from threads of melted glass was certainly known and talked about in a close scientific circle of experimenting savants (a short history of the spherical glass here). Among those notables were Spinoza’s correspondent Johannes Hudde who made them at least since 1663 when he showed his design to the French diplomat Monconys, and possibly used it as early as 1659 when he youthfully writes in a letter how he will uncover the secrets of generation through its powers. The scholar Vossius has one in 1663 which he also shows to Monconys, and in 1666 publishes the claim that the smaller the lens the stronger the magnification. And then to greatest attention Hooke describes his own bead microscope in the Micrographia in 1665 (some comments here), complaining though that it is too difficult to regularly use, fearing the loss of his eyesight.

Hooke's Fly's Eye, from the Micrographia

And of course, it is the king of all microscopists, Van Leeuwenhoek, who exclusively employed this kind of microscope, making over 500 of them almost all for his personal use (some comments here). When he began using them is of much debate. He makes a claim late in life that had had made bead microscopes as early as 1659 (so simple are they to make!), yet some scholars find him to have been directly informed by the description left by Hooke in the Micrographia. We do not hear of his use until 1774, and the nature of his microscope he keeps secret for sometime. It is Van Leeuwenhoek’s microscope – upon the reading of his 18thletterto the Royal Society, the day after Spinoza’s death – that will suddenly take center stage through its discoveries (although its nature at this time remains largely unknown). The single lens microscope is the strongest microscope in the world, but only now will Christiaan Huygens be coming to realize it.

For many years it seems Johannes Hudde had to defend his tiny spherical lenses against Huygens’ intution that larger, compound scopes would do a better job. It seems quite likely that Spinoza found himself mostly on the Hudde side of the argument, even I think it likely that it was Hudde himself, or one in his circle who disseminated the technique to him, either in Amsterdam or at Leiden. To this possibility, the famed Leiden anatomist Swammerdam attributes Van Leeuwenhoek’s technique to Hudde, as he does his own’ and Borch in his diary mentions the heavy influence of Hudde upon these Cartesians. Apart from this debate, Christiaan as a user of the compound scope as late as January 1675 to Oldenburg expresses an outright pessimism towards Van Leeuwenhoek discoveries already relayed to the Royal Society. These may be founded on his own frustrations when attempting to repeat the experiments, as he simply did not have enough magnification power, or they may even be a product of Van Leeuwenhoek’s low social standing as a mere draper in Delft (while Christiaan does not strictly know what kind of microscope Van Leeuwenhoek possesses, he may have guessed. There may be a class issue that folds into the conception of the microscope. Bead lenses are simply, too simple. They are not the shiny, gearing tubes of an upper machinery):

I should greatly like to know how much credice Mr. Leeuwenhoek’s observations obtain among you. He resolves everything into little globules; but for my own part, after vainly trying to see some of the things which he sees, I much misdoubt me whether they be not illusions of his sight…(Dobell 172)

Christiaan Huygens Makes His Turn

But back to the excitment. Something has turned Christiaan Huygens’ pessimism of the simple microscope into an enthusiasm. Most certainly some of this can be attributed to the sudden notability of Van Leeuwenhoek’s discovery of the protozoa and bacteria in marshy and boggy water. In November he will have discovered what male semen looks like under high magnification. At stake were arguments over just how Life itself was generated. (Did it arise spontaneously as it seemed to do in moulds, or was there some “mechanism” to it?) One can imagine the primacy of such a question. Secondly though, it is thought that Christiaan Huygens’s sudden leap towards the simple microscope was nearly entirely triggered and faciliated by the young microscopist Hartsoeker, who not long too before had discovered this technique for himself. The two were in correspondence and in March 1678 Hartsoeker reveals to him his secret. As Edward Ruestow narrates in his wonderful history The Microscope and the Dutch Republic:

The announcement of the discovery of spermatozoa in the fall of 1677 arouses the particular interest of Christiaan Huygens and, through the young Hartsoeker, drew him belatedly to the bead microscope…but having heard of a young man in Rotterdam whose microscopes could reveal the recently discovered spermazoa, Christiaangot in touch with Hartsoeker.

The essential account of their first contact, which is Hartsoeker’s, is tainted by its entanglement with his later claim that he had in fact been the first to discover spermatozoa. The surviving correspondence begins with a reply from Hartsoeker in March 1678 in which he explained how he made the bead with which he observed the “animalcules” found in semen. He presented Christiaan with a number of these sphericals, as well as some wood and brass devices to hold them in place, and by the endofthe month had himself come to The Hague to show Christiaan the spermatozoa of a dog. Hartsoekercontinued to correspond with Christiaan about the employment and improvement of these instruments, all of which Christiaan meanwhile shared with his brother Constantijn. The following year Constantijn spoke of Hartsoeker as “the inventor of our microscopes,” and years later Christiaan recalled Harksoeker having taught them to make little spheres that served as lenses (24-25)

This is all very convincing. Christiaan, after many years of resistance to the idea of tiny spherical lenses, debating with Hudde and possibily Spinoza, spurred on by the need for more powerful magnfication due to the discovery of protozoa, bacteria and then the most importantly, the elusive key to life, spermatozoa, collaborates with a savantish, largely unknown young man from Rotterdam who even claims that had discovered the technique himself when he was a young boy, and suddenly is applying his own rather vast device-making knowledge to craft the best microscopes in Europe, presenting them to the Paris academy, confirming Van Leeuwenhoek’s discoveries only three and a half months after having learned how to bead lenses himself. Huygens is shopping his microscope across the continent, while Van Leeuwenhoek refuses to allow anyone to look into or even see his.

But the problems with this quick reversal narrative is subtle. For one the lens-bead techique is extremely simple. Hartsoeker himself said he discovered it while toying with a thread of glass and a candle. Swarmmerdam says that he could make 40 more or less servicable bead lenses in an hour. It also, as I have said, was rather ubiquitous. To recount: Huddehadbeen in possession of it at least since 1663, was willing to depart with it for at least Swammerdam and Monconys, andin fact had discussed its advantages with Huygens in April 1665. As M. Founeir describes Huygens’ objection to Hudde:

Hudde discussed the merits of these lense with Huygens [OCV, 308-9, 318, 330-1], who declined their use. He particularly deplored their very limited lack of depthof field. He foundit inconvenient that with such a small lens one could not see the upper and underside of an object, a hair for instance, at the same time (“Huygens’ Design…” 579).

Vossius, Huygens’s friend seems to be in possession of it then, and it is no doubt related to the “flea glasses” that Descartes speaks of in 1637, “whose use is quite common everywhere”. Further, of course, when Hooke describes it in brief in his 1665 Micrographia, he exposes the method to the whole English reading world. This text Huygens remarkably had in his possession very soon after its publication, one of the few copies in Europe despite the Anglo-Dutch war of that year; and we have that copy, a section of which is annotated with Huygens’ hand. Huygens had even been so kind to actually translate some of the English for Johannes Hudde.

Further in evidence that Christiaan Huygens was well-familliar with this lens, in November 1673 Hooke demonstrates to the Royal Society “microscope with only one globule of glass, fastened to an instrument with many joints” likely made in wide production by the Dutch instrument maker Musschenbroek. And even more conclusively, Christiaan’s own father Constantijn Sr. a few months later writes of a powerful “machine microscopique” used by both Swammerdam and Leiden professor of Botany Arnold Seyn (Ruestow, 24 n.96); and we know that Swammerdam later favored a single lens scope. Given their prevalence, simplicity andthe extent of Huygens’ likely intercourse with these lenses, it could not be that Christiaan Huygens and his brother were somehow deprived, waiting to be told how to bead glass by the 22 year old [Leiden student?] Hartsoeker? It may be imagined that perhaps Hudde kept his personal means of grinding tiny lenses secret from Huygens due to some competitive antagonism and Huygens’ obstinancyover the larger, compoundlens microscope design. Perhaps. But it could not be that all of educated Europe keep it a secret from one of the foremost scientific minds of the time. Something does not sit right. Was it simply Huygens’s disinterest in such a low-depth of field, simple lens, andhis proclivities for certain other types of lens formations (compound, like his telescopes) that kept him from wanting to know? Was Hartsoeker simply the expedient when Christiaan needed to catch up quickly? The way that Edward Ruestow tells it we get the sense that it merely took the interest of Huygens, the timely injection of technique, and then the application of the Huygens’ brothers marvelous technical sense. Perhaps.

But I suggest that one piece is missing from this puzzle. It may be not until the Huygenses acquired the lens-grinding equipment and lens examples from Spinoza’s estate that they possessed the technical means of polishing these small spherical bead lenses: a talent for minute polish which Spinoza had showed early on. Could it be that this was the link, the technical means which accelerated the rapid development of the Huygens microscope from concept to actuality?

The Huygens droplet design, as it ended up in late 1678

Ruestow cites the kinds of changes that the Huygens brothers made to the Hartsoeker lens technique, such as “removing the molten globule from the thread of glass withametal wire, or, with one end of the wire moistened, picking up small fragments of glass to fuse them into globules over the flame” (25). All these seem aimed trying to make the sphere smaller and smaller, increasing its magnification. In the endChristiaan would proclaim to his French audience that his microscope is not much different than those in Holland and England, other than the size of its smaller lens, supposedly something which he alone had achieved.

He also produced a casing that was built around this tiny lens, “mounting their own beads in small squares of thin, folded brass; with the bead trapped between the opposing holes pierced with a needle through the two sides of the folded brass, those sides were pinched together with hammered pieces of wire. The microscope would go through several revisions.

As Ruestow writes of its appearance in Paris:

“on July 16th he presented to the assembly the ‘new microscope’ he had brought back withhim from Holland – one that, according the the academy minutes, was ‘extraordinarily small like a grain of sand’ and magnified incredibly…before July was out, Christiaanusedthe instrument to show the members of the academy the microscopic life Leeuwenhoek had found in pepper water, soon after publishing the first public announcement of their discovery in the Journal des Sçavans, Christiaanalsoidentified it with the discovery of the spermatozoa.”

By August his microscope had caused the “great noise” all over Paris, so much so that John Locke at Blois had heard of it. Through the next year he had “cultivated the impression” that Van Leeuwenhoek’s observations were made with a microscope like his own. French instrument makers set to copying his invention. The response was not altogether gleeful. In London Hooke was somewhat put out that so much excitment surrounded what for him was a well-known device, one that he himself had fashioned, used and written of. And Hartsoeker, having finished his third year at the University at Leiden, all the while had been left in the shadows, not something that sat well with his rather conceitful temperment. Traveling to Paris Hartsoeker sought in some way to unmask his role in the creation of this remarkable device, exposing Huygens to be something of a plagerist. As Ruestow reports, knowing wisely Christiaan steered him from that course,

but [Christiaan] quickly took his younger compatriot under tow and wrote a brief report for him, published in the influential Journal des Sçavans, that asserted Hartsoeker’s active role in making new bead microscopes (27).

We have here evidence of Christiaan’s tendency to obscure the origins of his microscope. Yet was there more to the development than simply Hartsoeker’s revelation of the thread melting techique? Was it that in the purchase of Spinoza’s lens-polishing equipment they acquired something of the techiques long appreciated by the brothers? Does this technique prove essential to Christiaan’s implementation of a rather simple bead-glass lense? Was Hartsoekersimply solicited for the one remaining aspect of the technique that Spinoza’s equipment would not provide, that of simply melting the glass into a lens? We do know that the grinding of the already quite spherical bead was common among its users. For instance Van Leeuwenhoek ground and polished almost all of his tiny bead lenses, (and modern assayers do not quite know why). Further, Johannes Huddealsopolished his bead lenses, reportedly with salt. Was there something to Spinoza’s knowledge of small lens-crafting that facilitated Huygens’ suddenly powerful microscope design? Something even that Hartsoeker was privy to? And lastly, if Spinoza’s equipment and techniques are implimented in this sudden rise of the simple microscope, what does this say about Spinoza’s own microscope making practices.

All this fantastic story is just speculation of course

It could merely be a coincidence that, with Spinoza having died just as protozoa and bacteria were being discovered; and with his equipment coming into the hands of the brilliant Huygenses almost 9 months later, they they then just happen to be aided by a young microscopist that gives the means needed to suddenly develop a microscope that will sweep across Europe in merely a few months. Christiaan Huygens and his brother were brilliant enough for that. Perhaps Spinoza’s ginding dishes and recipes simply sat in the dust, having been acquired. But it should be noted that many years before this, the physcian Theodor Kerckring, a friend of Spinoza’s and a member of the inner, Cartesian circle, son-in-law to its central member Franciscus Van den Enden, writes of his use of Spinoza’s microscope:

“I have to my disposal a very excellent (praestantissimum) microscope, which is fabricated by that noble Benedictus Spinosa, mathematician andphilosopher…What I in this way discovered with the help of this admirable instrument…[are] endless many extremely small animalcula….”

This is found in his Spicilegium anatomicum published in 1670, seven years before Van Leeuwenhoek’s acclaimed description of the protozoa and bacteria in letter 18. It is not clear at all what “animalcula” Kerckring saw (some offer that they are post-mortum microbes, or mistaken ciliated action), but there is the possibility that these were the earliest microorganisms to be described, or at the very least, Spinoza had perfected an advanced form of the single lens, bead-microscope whose powers of magnfication approached many of those of Van Leeuwenhoek, and even that of its copist Christiaan Huygens. The timing remains. In November of 1677 the Huygenses lmay have acquired Spinoza’s lens grinding equipment, and in 8 months they have a microscope of remarkable powers.

Some discussion has been going on over at the Practical Machinistforum, where I have sought any views about the real world workings of any of the devices Spinoza may have used at grind lenses. I have come to the thought that it might very well be a rather simple device that Spinoza used, not much differnt than the one Manzini depicts for the start of the 17th century:

In response to my query someone was kind enough to relate some of his own, unique experiences with a machine not unlike the one illustrated. I post them here because they serve to vivify the elementary nature of these technical movements, in the manner of which a 20th century workman and a 17th century philosopher might share an experience of material and design effects.

Joe writes:

When I was in my 20s I worked for a couple of years at the Peerless Optical Co in Providence, Rhode Island, making lenses for glasses. While much of the work was automated to a degree there was still a little corner of the shop where very special lenses were ground. Because I was actually interested in the work, that became my department.

The lenses were ground against iron forms, called “laps” (either convex or concave) using a variety of progressively finer abrasives. The final polish was achieved by gluing a thick disc of felt to the lap and using a much finer polishing media. The lap spun in a bucket-like contraption that worked very much like a potters wheel. The lens was kept in contact with the lap by means of a hinged arm with an adjustable pin. The arm was held in place with the left hand, the pin pushing against the lens, while you added abrasive to the lap with the right hand. To secure the lens without damaging it, a small flat piece of metal with a center hole was “glued” to it using thick green pitch, exactly like the “sealing wax” used before the invention of gummed envelopes. We melted the pitch onto the lens with a bunsen burner. It was removed by chilling the whole piece, at which point the pitch would harden and fall off the glass.
Other than the motor that spun the lap, there isn’t a thing about this whole process that any 17th century mechanic would find surprising. Also, with particularly difficult lenses, I would have to forgo the hinged arm and hold the lens against the lap with my hand.

In our case, a special purpose-built machine re-cut the laps when they wore…I had a beautiful engraved set of brass gauges which I used to check them (by holding the gauge and lap up to a window) and which must have been 100 years old or more when I was using them. I can see where a lathe of some sort would be essential for making the laps, a primative lathe would suffice, but I can’t see it being used to actually make the lens itself.

The machine illustrated in the post above this one is very much like what I am describing. In fact, other than the hand operation it would be instantly recognizable to anyone who was making lenses in the manner I was. I actually made a couple of lenses for an antique telescope on this equipment…they worked perfectly.

In coincidence to this, Rijk-Jan Koppejan sent me a photograph of a reproduction of just this illustrated device, built by his team and part of their exposition on the invention of the telescope, organized around the 400th year Middelburg anniversary. There is to be a symposium of speakers in September, which I just may have to find a way of attending. He says he may be able to take new, more revealing photographs and send them. I will post them as he might.

Joe mentions that the curvature of this grinding “dish” may be too extreme, but that Manzini’s illustrator may not have thought this a significant factor (also, we cannot see the internal curavature of the reproduction). I don’t know enough about the optics of the time to comment.

He mentions as few more interesting details of his memory of lens grinding with such a lathe, in particular the method he had to use to correct the wear on the “laps” (as he calls them) – Spinoza calls them patinas or scutellae, plates or dishes – and thoughts about processes by which a spherical lens is checked for its optical quality:

I suspect that the drawback to using male/female laps against each other is that both pieces will wear. I am guessing that if the lens maker had a set of gages like I used, which are simply used to check the curve, the lap could be spun in any lathe-like machine and the surface selectively filed or ground to return it to true. As I’ve said, I held the lap and the gage up to a window and looked for a streak of light between them…a very accurate way of measuring once you have some practice and know what to look for.

…Another memory just came back…I think that the felt was attached to the lap with fish or hide glue. The lens was checked by holding it up to a light bulb with a single filiment. You held it in such a way that the light from the filiment reflected off the surface. If there were no breaks or nicks in the reflection, the lens was perfectly true. This could also be done by stretching a hair across a window and picking up the shadow. You could never see the imperfections with the naked eye..

…The lens was finished in what we called an “edger” which was nothing more than a lathe-like spindle that gripped the little metal piece glued to the lens and spun it against a grinding wheel. These were not the modern clay-based wheels but slow turning natural stone wheels that ran in water, the grinding wheel turning one way and the lens in the opposite direction. In this way the outer edge was gradually reduced in a manner perfectly concentric with the optical center. Even if the metal attachment was slightly off center on the original lump of glass, this process insured that it would be perfectly concentric when finished. You could only remove the metal piece after this was done and you could not replace it perfectly so it was a once-chance-only affair.

Althought at this point it is only a collective intution that Spinoza did not use a large, spring-pole lathe such as the one shown at the Rijnsburg, there are some facts that lead to me this thought. First is that when Huygens writes of the superior polish of Spinoza’s lenses, he describes them as “little lenses”:

“the Jew of Voorburg finishes his little lenses by means of the instrument and this renders them very excellent” (Complete Works, 6:155).

I do not have the original word from which “instrument” is translated, but at least at this point it strikes me that this is a small device. And these lenses are small. I am unsure if Huygens is talking about telescope lenses or microscope lenses, but there is the implication of very fine work. This also coincides with Spinoza’s own light criticism of Huygens’ very complex machine, in letter 32 to Oldenburg. (See some of my thoughts on this here.) It is of course possible that Spinoza had a spring-pole lathe much like the Rijnsburg and Hevelius lathes, but the contrast between his own approaches and Huygens’s seems more at home with a simpler device. There are other factors that cause me to think that this is so, but for now this is enough to discuss.

I was discussing with my wife this developing idea that Spinoza’s metaphysical work needs to be understood in light of the specific practices and techniques he engaged in as a lens-grinder. I was busy describing to her how physical the act of lathing is, the dynamics of its transformations, and how when one watches it, seeing it, simply thinking of it as an act of grinding, or in terms of the materials used, is insufficient.

She came up with one of those apt analogies, which are particular to her mind, saying something of the order, “Yes, it would be like knowing what clay is, and even understanding what a potter’s wheel might be, but having never seen it in action”. I think that she is very right. We think of Spinoza as a lens-grinder, perhaps see him hunched over a workbench, vaguely picturing his hands cusped, pressing something hard and small against something spinning. Maybe we hear in the background the requisite sound of grinding, something metal on metal. But none of this really is what the picture-of-the-world of lathework provides. There is something potters-wheel-like in the combination of changes faster than the eye can see, amid a stability, a stability that communicates itself both despite and because of change. It embodies, in a very real way, what conceptually can only read as paradox, natura naturata and natura naturans. In it conflict and pressures create forms that rise out of an unformed, and the physicality of “idea” is not so much a theoretical and abstract position, as a real and experienced fact. Perhaps this is what he meant by his “demonstration” of the “eyes of the mind”.

If a philosopher were a full-time potter, it would serve to look to the potter’s wheel and its effects as a source of conceptual inspiration. So with the lathe, the pan and the glass.

I think that if anything, Spinoza’s metaphysics, the equanimity with which he treats the material world, never letting it fall to the inferior position, insists upon a craftsman’s understanding of the world, and what practically must be done. We are mislead, I believe, due to the Idealism that followed after Spinoza, into thinking about Idea even in the case of Spinoza, in an etherial, and not so much an informational sense. Further, the technical, the engined, if guided by Spinoza’s hand, must be understood as craft. If one watches a lathe, and thinks in Spinoza’s terms, one sees the world spin and fix.

In Spinoza’s letter (15/32) to Royal Society secretary, Henry Oldenburg, after a summary of the reasons why Spinoza believes that “each part of nature agrees with its whole,” in which our knowledge position is compared to that of a worm living in our blood, the letter finishes with a few seemingly mundane topics, one of which is on Oldenburg’s interest in scientist Christiaan Huygens’s work. It is a passing note, but telling, both in its tone and substance:

The said Huygens has been a totally occupied man, and so he is, with polishing glass dioptrics; to that end a workshop he has outfitted, and in it he is able to “turn” pans – as is said, it’s certainly polished – what tho’ thusly he will have accomplished I don’t know, nor, to admit a truth, strongly do I desire to know. For me, as is said, experience has taught that with spherical pans, being polished by a free hand is safer and better than any machine.

In terms of tone, we get a sense of what Spinoza thinks of the wealthy Huygens’s fabrica. The shop has been fully furnished [ adornavit ] and perhaps Spinoza’s humorous word-play is evident as he calls it nitidam, a shiny, glossy or polished thing. It is a workshop for polishing lens, and itself is quite polished: spiffy. We can feel a contrast to Spinoza’s much more humble abode and hand-polishing buisness. He is the still the merchant thinker, the “Jew of Voorburg” (a village outside The Hague) or at times the “Isrealite” whose small lenses have a “remarkable polish”, in the mind of Huygens. Huygens, at the cusp of a mechanical age when the machines still have the aura of the divine about them, is pursuing a mechanized way of producing lenses, one that Spinoza cannot embrace at quite a few levels.

Also interesting is that there seems some lexical ambiguity which obscures just what is being turned. Is it the patinae (templates), or is it the patinae (understood as “tools”)? There are various descriptions of the full lathing process. By Cherubin’s report (1671), which may be rather late, and more complex than usual, there are three stages to lens-making: turning, grinding, and polishing, all of which though can be called “turning”. Turning first involves the making of templates proably made of iron, but in Huygens’s case may even be made of the superior material brass. Two are made in a convex/concave pair, and these are ground against each other to insure sphericality. These turned metal templates are then used to grind and polish a pair of brass or iron “tools” which are then used to grind and polish the glass blank. It seems the case that what Huygens’s workshop is capable of is not only polishing lenses, but also of grinding tools, and even perhaps turning the templates themselves. There is some evidence that the turning of the template was in the case of spectacle making done by a guilded turner (17).¹ So it is not perfectly clear enough if the patinae are templates or tools. But what does seem clear is that Huygens’s is a kind of impressive all-in-one machine, or workshop, one that does more than the usual. This is also suggested from his notebook drawings from the period. Possibly, everything from the work of the turner on to the final glass product can be achieved. [Spinoza, by the evidence of his letter to Hudde shown below, at least at the time of the writing of that letter, may have not only had his patinae (templates or tools) made for him, but perhaps even both, as he there uses the term scutellae (dishes), which are to be fashioned by someone else. Whether this term is synonymous with patinae is undecided.

In the latter half of our considered passage the image becomes potentially more complex. It is commonly translated and understood that Spinoza is talking about his experience with polishing of the patinae (templates/tools) themselves. Perhaps. Yet, in patinis sphaericis really gives the perspective of the polishing being carried out in respect to the use of patinae – perhaps even “within pans”, as in: “being polished by a free hand in spherical pans, is safer and better”. A free interpretation of the Latin does not easily produce the idea that the polishing is solely being done to the pans themselves. This is further supported, I believe, by the passive form of the infinitive expoliri. The sense is that being polished by the means of a free hand (the technique for hand-holding a glass blank, or any polishing device onto the pan) is both safer and better, with the infinitive operatating as the subject of the clause.

These are of course tentative thoughts about this passage, but it seems that instead of reading Spinoza’s comments as pertaining only to his long-time experience of polishing metal pans – patinae – Spinoza seems to be talking instead about his preference for using a free hand for glass itself, in metal forms. This matches up with the known fact that Huygens’s machines were ones that held the glass blank fixed in some mechanically guided way, put against the form as part of the final process. It makes more sense for Spinoza to be responding to this semi-automated, glass-grinding aspect of Huygens’ machine, and not just a form-polishing technique. The entire mechanism is organized in a way that defies Spinoza’s experienced wisdom of grinding and polishing.

Lastly, by specifying the sphericality of the patinae, he is also setting himself against any of the much-pursued quests for a way to mechanically produce Hyperbolic Lenses, (initiated by Descartes own discovery of a law of refraction, his own belief that the Hyperbola was a revealing form). Not only is Spinoza commenting upon Huygens’s social affluence, in an off-hand way, but also upon any non-spherical lens aims, and the idea that an insensate hand could create the fineness of results needed.

Here is Elwes’ translation of the passage:

The above-mentioned Huyghens is entirely occupied in polishing lenses. He has fitted up for the purpose a handsome workshop, in which he can also construct moulds. What will be the result I know not, nor, to speak the truth, do I greatly care. Experience has sufficiently taught me, that the free hand is better and more sure than any machine for polishing spherical moulds. I can tell you nothing certain as yet about the success of the clocks or the date of Huyghens journey to France.

And Shirley:

The said Huygens has been, and still is, fully occupied with polishing dioptical glasses. For this purpose he has devised a machine in which he can turn plates and a very neat affair it is. I don’t yet know what success he has had with it, and, to tel the truth, I don’t particularly want to know. For experience has taught me that in polishing spherical plates a free hand yield safer and better results than any machine.

I hesitate of course to re-translate such esteemed translators, but it seems that there are good arguments for reading Spinoza’s meaning another way. At the very least, the possibility of a second meaning seems present.

For evidence that Spinoza himself did not fashion his own templates (and perhaps not even his own “tools”), from the letter to the mathematician Hudde (41/36):

“With these I may have ended, in truth, but because for me new dishes for glasses being polished may be fashioned, such is the spirit, your council in this matter I would be eager to hear. I do not see what we may profit in ‘turning’ convex-concave glasses.”

“I might have ended here, but since I am minded to get new plates made for me for polishing glasses, I should very much like to have your advice on this matter. I cannot see what we gain by polishing convex-concave glasses” (trans. Shirley: likely June 1666; page 142 Opera).

It does not seem likely that Spinoza had very much experienced, first hand, the safety of fashioning metal plates (it may of course be the case that though not fashioning them, he did polish them, but then the safety of the process – mentioned in the letter to Oldenburg – would seem to be less of an issue). To sum up, it seems more the case that Spinoza is, first, noting the furnished and “spiffy” nature of Huygens’s fabrica, as it polishes lenses (and even patinae ), and then secondly, that Spinoza is referring to and judging a more particular aspect of Huygens’s machine – one well-known, since Huygens was working on a semi-mechanized process for polishing lenses for a decade – that the glass is not held in a free hand.

I have begun my study of the lens-grinding practices of Spinoza, and how they may have helped structure his non-Cartesian conception of Representation, and metaphysics. I will not be reporting the preponderance of my discoveries here, saving them for an article in process, but already efforts are paying off. Very little has been written on Spinoza’s lens-grinding, and almost no scholarly study has been conducted as to these connections, so this is, as far as I can tell, conceptually virgin ground in Spinoza studies.

For those who do not have a vivid conception of what lathe work is, and the basic dynamics involved, posted above is a youtube video which shows a foot-powered lathe that is not in principle distinct from the lathe that Spinoza must have used (as of yet, I cannot ascertain if it was likely to be hand or foot powered). As one can see, the rotational power of the lathe provides a concentric force for shaping material evenly, and spherically. Most broadly, it is assumed that Spinoza as a lens-grinder would by hand hold the lens blank against a rotating metal “pan” patina, which previously had been shaped into a mould form. A variable grit recipe of abrasives is placed in the pan during grinding, to aid in the shaping, and then polishing, of the lens.

Here is the eariliest illustration of lens-lathing, from a 17th century work of optics (woodcut from Manzini):

Pictured is a torino in aria, a “turner in air” device, so named because the lens had to be held high, above the eyes (there is of course a rhetoric of ascension). If it is unclear, the right hand turns a crank, which sets a vertical belt in motion, which itself turns a horizontal axis above, at whose end is a hemispherical pan, into which the left hand inserts a glass blank, itself cemented to a handle for easy grasping. This early Italian model was most likely modified by the time of Spinoza’s practice, so that the lens was held lower down, at a table or a bench. Its basic mechanics were the same.

A Reconsideration of Spinoza’s Definition of an Individual

But, for a moment, let us consider how just this motion of grinding a hand-held object against a rotating and grinding circular surface imparts to us additional information for how Spinoza conceived his various propositions, and intended them to be understood. (For it is often that a picture of the world and its relations, is that which guides our claims and descriptions).

What I have in mind, is Spinoza’s very interesting definition of what a “body” is. It is a definition I have often thought that I have understood, and even have used in my own arguments. But somehow here, with the dynamics of this technical process shedding their light upon Spinoza’s metaphysics, this Defintion comes to life in a new way:

Definition: When some bodies of the same or a differing magnitude apart from what remains [ a reliquis ] are so controled that reciprically [ invicem ] they may press against [each other], or if they with the same or diverse speeds by degrees are moved so that their motions through some fixed rule [ certa quadam ratione] reciprically they communicate; those bodies, reciprically, are united we say, and they all at once [simul ] one body or Individual compose, which through this bodily union is distinguished apart from what remains [ a reliquis ].

-Ethics II, Lemma 3, Axiom 2″, Defintion

I include Curley’s, largely taken to be precise, translation of the same passage, for interpretive comparison, most notable is his inconsistent translation of the phrase “a reliquis“; in the first half of the definition is left under-translated as an agent “other bodies”, and then in the latter half, as an ablative of separation. The notions of “remainder” [ reliquis ] and “alternate turns” or recipricality [ invictem ] when seen in view of a mechanical process can have greater meaning:

Definition: When a number of bodies, whether of the same or different size, are so constrained by other bodies that they lie upon one another, or if they so move, whether with the same degree or different degrees of speed, that they communicate their motions to each other in a certain fixed manner, we shall say that those bodies are united with one another and that they all together compose one body or Individual, which is distinguished from the others by the union of bodies.

Aside from the particularities of translation, this has always been a spectacular definition of what an Individual is, for it freed up our concept of what it means to combine and act as a whole. Thereby, any ratio of speeds and communicated motions, such that it preserves itself, suddenly becomes a “body”. The entire world opens up to such transitions, of concrete things coming into a fixity of ratios and passing out, such that the boundaries of bodies, and their definitions, becomes fluid and I think cybernetic. For instance, my car and myself, as I drive it, fall under this notion of an “Individual” making Spinoza applicable to the post-industrial times.

But when we picture this definition of communicated motions and fixed manners in the specificity of a lens-grind lathe, something more comes about. To the human eye, as it turns the finishing pan strikes one as quite distinct from the lens on which it acts. It is spinning and the lens is relatively fixed. But the two in their communication of their motional states in a fixed manner – the idea of the mathematical calculation, the rule which determined the shape of the pan – come together. Two objects have been brought into a particular relation, under a rule. Here the differential of the degree of speed, under a constraint, allows the ratio of their fixity – a certain stillness, an eternity – to be partaken of, which makes of the two, one thing, a composite. We can leave aside for the purposes of a simplicity of illustration the sensate figure of the human craftsman who is fixing the lens, yet turning the lathe, a figure which necessarily must be worked into the cybernetic model of a communication of speeds and parts. But between the two parts of the patina andvitrum a combinational process creates a single Individual, one which perhaps lies key to how Spinoza imagined his Ethics to be read and used. The rest of this passage on bodies and ratios and fluids also benefits from just this technical reading as well.

Ode to Man

Tho’ many are the terrors,
not one more terrible than man goes.
This one beyond the grizzled sea
in winter storming to the south
He crosses, all-engulfed,
cutting through, up from under swells.
& of the gods She the Eldest, Earth
un-withering, un-toiling, is worn down,
As the Twisting Plough’s year
into Twisting Plough’s year,
Through the breeding of horse, he turns.
& the lighthearted race of birds
all-snaring he drives them
& savage beasts, their clan, & of the sea,
marine in kind
With tightly-wound meshes spun
from all-seeing is Man.
Yet too, he masters by means of pastoral
beast, mountain-trodding,
The unruly-maned horse holding fast,
‘round the neck yoked,
& the mountain’s
ceaseless bull.
& the voice & wind-fast thought
& the passion for civic ways
He has taught, so from crag’s poor court
from under the ether’s hard-tossed arrows
To flee, this all-crossing one. Blocked, he comes
upon nothing so fated.
From Hades alone escape he’ll not bring.
Tho’ from sickness impossible
Flight he has pondered.
A skilled one, devising of arts beyond hope,
Holding at times an evil,
But then to the noble he crawls,
honoring the laws of the Earth, &
Of gods the oath so just,
high-citied.
Citiless is the one who with the un-beautiful
dwells, boldly in grace.
Never for me a hearth-mate
may he have been, never equal in mind
He who offers this.

Ode to Man

A BwO is made in such a way that it can be occupied, populated only by intensities. Only intensities pass and circulate. Still, the BwO is not a scene, a place, or even a support upon which something comes to pass. It has nothing to do with phantasy, there is nothing to interpret. The BwO causes intensities to pass; it produces and distributes them in a spatium that is itself intensive, lacking extension. It is not space, nor is it in space; it is matter that occupies space to a given degree—to the degree corresponding to
the intensities produced. It is nonstratified, unformed, intense matter, the matrix of intensity, intensity = 0; but there is nothing negative about that zero, there are no negative or opposite intensities. Matter equals energy. Production of the real as an intensive magnitude starting at zero. That is why we treat the BwO as the full egg before the extension of the organism and the organization of the organs, before the formation of the strata; as the intense egg defined by axes and vectors, gradients and thresholds, by dynamic tendencies involving energy transformation and kinematic movements involving group displacement, by migrations: all independent
of accessory forms because the organs appear and function here only as pure intensities. The organ changes when it crosses a threshold, when it
changes gradient. "No organ is constant as regards either function or position, . . . sex organs sprout anywhere,... rectums open, defecate and close, . . . the entire organism changes color and consistency in split-second adjustments." The tantric egg. After all, is not Spinoza's Ethics the great book of the BwO?

Ode to Man

But human power is extremely limited, and is infinitely surpassed by the power of external causes; we have not, therefore, an absolute power of shaping to our use those things which are without us. Nevertheless, we shall bear with an equal mind all that happens to us in contravention to the claims of our own advantage, so long as we are conscious, that we have done our duty, and that the power which we possess is not sufficient to enable us to protect ourselves completely; remembering that we are a part of universal nature, and that we follow her order. If we have a clear and distinct understanding of this, that part of our nature which is defined by intelligence, in other words the better part of ourselves, will assuredly acquiesce in what befalls us, and in such acquiescence will endeavour to persist. For, in so far as we are intelligent beings, we cannot desire anything save that which is necessary, nor yield absolute acquiescence to anything, save to that which is true: wherefore, in so far as we have a right understanding of these things, the endeavour of the better part of ourselves is in harmony with the order of nature as a whole.